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Displaying 381 –
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We present a method for estimating the edge of a two-dimensional
bounded set, given a finite random set of points drawn from the interior.
The estimator is based both on a Parzen-Rosenblatt kernel and
extreme values of point processes. We give conditions
for various kinds of convergence and asymptotic normality.
We propose a method of reducing the negative bias and edge effects,
illustrated by some simulations.
The extremal shape factor of spheroidal particles is studied. Three dimensional particles are considered to be observed via their two dimensional profiles and the problem is to predict the extremal shape factor in a given size class. We proof the stability of the domain of attraction of the spheroid’s and its profile shape factor under a tail equivalence condition. We show namely that the Farlie–Gumbel–Morgenstern bivariate distributions gives the tail uniformity. We provide a way how to find normalising...
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